A discrete factor graph is a directed acyclic bipartite graph representing the factorization of a joint probability distribution. The nodes of the discrete factor graph are random variables with discrete values (e.g., Booleans, categories, intervals, or integers). The edges of the discrete factor graph represent causal relationships between the connected random variables. The factors of the discrete factor graph define conditional probability distributions of the random variables with matrices.
Realistic factor graphs for applications may have hundreds of nodes for which information is gathered from distinct sources. Sub-graphs may be created for each group of nodes corresponding to each of the distinct sources, but it is difficult to combine the separate sub-graphs into a coherent and conflict-free factor graph.